if `x<1` then `1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+..............oo`

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-x, a+x, a-x],[ a-x, a-x, a+x]|=0

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

If f(x)=|[x+lambda,x,x] , [x,x+lambda,x] , [x,x,x+lambda]| then f(12x)-f(x)=

If f(x) is continuous at x=a,a>0, where f(x)=[(a^x-x^a)/(x^x-a^a), for x!=a, -1 for x=a, then a=

If 5{x}=x+[x] and [x]-{x}=(1)/(2) when {x} and [x] are fractional and integral part of x then x is

If f(x) = |[x+p,x+a,x+a],[x+b,x+q,x+a],[x+b,x+b,x+r]| and g(x)=(p-x)(q-x)(r-x) , then the value of f(0) is

simplify (x+x^(2)+x^(3)+x^(4)+x^(5)+x^(6)+x^(7))/(x^(-3)+x^(-4)+x^(-5)+x^(-6)+x^(-7)+x^(-8)+x^(-9))

Lt_(x rarr0)x+(sin x)/(x+(sin x)/(x+(sin x)/(x+(sin x)/(x+(sin x)/(x+mu x))))=)